Trigonometry Examples

$\sec (- \frac{π}{3}) - \cot (- \frac{5 π}{4})$

Step 1

Simplify each term.

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Step 1.1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sec (\frac{5 π}{3}) - \cot (- \frac{5 π}{4})$

Step 1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sec (\frac{π}{3}) - \cot (- \frac{5 π}{4})$

Step 1.3

The exact value of $\sec (\frac{π}{3})$ is $2$ .

$2 - \cot (- \frac{5 π}{4})$

Step 1.4

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$2 - \cot (\frac{3 π}{4})$

Step 1.5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cotangent is negative in the second quadrant.

$2 - - \cot (\frac{π}{4})$

Step 1.6

The exact value of $\cot (\frac{π}{4})$ is $1$ .

$2 - (- 1 \cdot 1)$

Step 1.7

Multiply $- (- 1 \cdot 1)$ .

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Step 1.7.1

Multiply $- 1$ by $1$ .

$2 - - 1$

Step 1.7.2

Multiply $- 1$ by $- 1$ .

$2 + 1$

Step 2

Add $2$ and $1$ .

$3$